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Print the degree of every node from the given Prufer sequence

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  • Difficulty Level : Hard
  • Last Updated : 22 Jun, 2022
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Given a Prufer sequence, the task is to find the degrees of all the nodes of the tree made by the prufer sequence.
Examples: 
 

Input: arr[] = {4, 1, 3, 4} 
Output: 2 1 2 3 1 1

The tree is:
2----4----3----1----5
     |
     6 

Input: arr[] = {1, 2, 2} 
Output: 2 3 1 1 1

 

A simple approach is to create the tree using the Prufer sequence and then find the degree of all the nodes. 
Efficient approach: Create a degree[] array of size 2 more than the length of the prufer sequence, since the length of prufer sequence is N – 2 if N is the number of nodes. Initially, fill the degree array with 1. Iterate in the Prufer sequence and increase the frequency in the degree table for every element. This method works because the frequency of a node in the Prufer sequence is one less than the degree in the tree. 
Below is the implementation of the above approach: 
 

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to print the degrees of every
// node in the tree made by
// the given Prufer sequence
void printDegree(int prufer[], int n)
{
    int node = n + 2;
 
    // Hash-table to mark the
    // degree of every node
    int degree[n + 2 + 1];
 
    // Initially let all the degrees be 1
    for (int i = 1; i <= node; i++)
        degree[i] = 1;
 
    // Increase the count of the degree
    for (int i = 0; i < n; i++)
        degree[prufer[i]]++;
 
    // Print the degree of every node
    for (int i = 1; i <= node; i++) {
        cout << degree[i] << " ";
    }
}
 
// Driver code
int main()
{
    int a[] = { 4, 1, 3, 4 };
    int n = sizeof(a) / sizeof(a[0]);
    printDegree(a, n);
 
    return 0;
}

Java




// Java implementation of the approach
import java.util.*;
 
class GFG
{
 
    // Function to print the degrees of every
    // node in the tree made by
    // the given Prufer sequence
    static void printDegree(int prufer[], int n)
    {
        int node = n + 2;
 
        // Hash-table to mark the
        // degree of every node
        int[] degree = new int[n + 2 + 1];
 
        // Initially let all the degrees be 1
        for (int i = 1; i <= node; i++)
        {
            degree[i] = 1;
        }
 
        // Increase the count of the degree
        for (int i = 0; i < n; i++)
        {
            degree[prufer[i]]++;
        }
 
        // Print the degree of every node
        for (int i = 1; i <= node; i++)
        {
            System.out.print(degree[i] + " ");
        }
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int a[] = {4, 1, 3, 4};
        int n = a.length;
        printDegree(a, n);
    }
}
 
/* This code contributed by PrinciRaj1992 */

Python3




# Python3 implementation of the approach
 
# Function to print the degrees of
# every node in the tree made by
# the given Prufer sequence
def printDegree(prufer, n):
  
    node = n + 2
 
    # Hash-table to mark the
    # degree of every node
    degree = [1] * (n + 2 + 1)
 
    # Increase the count of the degree
    for i in range(0, n):
        degree[prufer[i]] += 1
 
    # Print the degree of every node
    for i in range(1, node+1): 
        print(degree[i], end = " ")
      
# Driver code
if __name__ == "__main__":
  
    a = [4, 1, 3, 4]
    n = len(a)
    printDegree(a, n)
 
# This code is contributed by Rituraj Jain

C#




// C# implementation of the approach
using System;
     
class GFG
{
 
// Function to print the degrees of every
// node in the tree made by
// the given Prufer sequence
static void printDegree(int []prufer, int n)
{
    int node = n + 2;
 
    // Hash-table to mark the
    // degree of every node
    int[] degree = new int[n + 2 + 1];
 
    // Initially let all the degrees be 1
    for (int i = 1; i <= node; i++)
    {
        degree[i] = 1;
    }
 
    // Increase the count of the degree
    for (int i = 0; i < n; i++)
    {
        degree[prufer[i]]++;
    }
 
    // Print the degree of every node
    for (int i = 1; i <= node; i++)
    {
        Console.Write(degree[i] + " ");
    }
}
 
// Driver code
public static void Main(String[] args)
{
    int []a = {4, 1, 3, 4};
    int n = a.Length;
    printDegree(a, n);
}
}
 
// This code is contributed by 29AjayKumar

Javascript




<script>
 
// JavaScript implementation of the approach
 
    // Function to print the degrees of every
    // node in the tree made by
    // the given Prufer sequence
    function printDegree(prufer , n)
    {
        var node = n + 2;
 
        // Hash-table to mark the
        // degree of every node
        var degree = Array(n + 2 + 1).fill(0);
 
        // Initially let all the degrees be 1
        for (i = 1; i <= node; i++) {
            degree[i] = 1;
        }
 
        // Increase the count of the degree
        for (i = 0; i < n; i++) {
            degree[prufer[i]]++;
        }
 
        // Print the degree of every node
        for (i = 1; i <= node; i++) {
            document.write(degree[i] + " ");
        }
    }
 
    // Driver code
     
        var a = [ 4, 1, 3, 4 ];
        var n = a.length;
        printDegree(a, n);
 
// This code contributed by Rajput-Ji
 
</script>

Output: 

2 1 2 3 1 1

 

Time Complexity: O(N), as we are using a loop to traverse N times. Where N is the number of elements in the array.

Auxiliary Space: O(N), as we are using extra space degree array.


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